Adaptive quantum channel discrimination using methods of quantum metrology

We present an efficient tensor-network based algorithm for finding the optimal adaptive quantum channel discrimination strategies inspired by recently developed numerical methods in quantum metrology to find the optimal adaptive channel estimation protocols. We examine the connection between channel discrimination and estimation problems, highlighting in particular an appealing structural similarity between models that admit Heisenberg scaling estimation performance, and models that admit perfect channel discrimination in finite–number of channel uses.

💡 Research Summary

The paper introduces a tensor‑network based numerical method for finding optimal adaptive strategies in quantum channel discrimination, extending techniques originally developed for quantum metrology. The authors first formulate the discrimination task in the language of quantum testers (or combs), where the goal is to maximize the average success probability over an ensemble of channels given a fixed number of uses N. This formulation leads to a semidefinite program (SDP) that is exact but scales exponentially with N, making it impractical for large‑N scenarios.

To overcome this bottleneck, the authors decompose a general adaptive strategy into three types of tensors: an input state ρ, a set of inter‑channel control operations {E_n} (the “teeth” of the comb), and a final measurement channel M. By treating all but one of these tensors as fixed, they construct a reduced SDP that optimizes the remaining tensor while preserving the overall causal structure. The algorithm cycles through all tensors repeatedly, updating each one in turn until the improvement in the success probability falls below a preset threshold (typically ε = 10⁻⁴). Because each sub‑problem involves far smaller matrices, the method can handle many channel uses with modest computational resources.

Beyond the algorithmic contribution, the paper establishes a rigorous connection between channel discrimination and parameter estimation. For a binary discrimination problem where the two channels correspond to parameter values θ = 0 and θ = Δθ, the Helstrom bound p_success = (1 + D_tr)/2 can be related to the Bures angle D_A, which in turn is bounded by the quantum Fisher information (QFI) via D_A ≤ (Δθ/2)√F. This yields a lower bound on the error probability p_err ≥ ½